Time needed to algebraically solve system of $15$ nonlinear equations with parameters

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How long can I expect it will take to algebraically solve a system of $15$ nonlinear equations (without any numbers, only parameters), if I feed it into a computing software?

I'm asking for symbolic solving - is MAPLE, MATLAB, or Mathematica the best?

Here are the equations that I am talking about:

$$A - Ba - \frac{Va(c+d+t+s+h)}{z} - \frac{Wa(b+d)}{z} = 0$$

$$\frac{Wa(b+d)}{z} - \frac{Vb(c+d+t+s+h)}{z} - (B+D+GF)b = 0$$

$$\frac{Va(c+d+t+s+h)}{z} - \frac{Wc(b+d)}{z} - (B+E+C)c = 0$$

$$\frac{Vb(c+d+t+s+h)}{z} + \frac{Wc(b+d)}{z} - (B+C+D+F)d = 0$$

$$GFb - \frac{Ve(c+d+t+s+h)}{z} - (B+H)e = 0$$

$$He - \frac{Vf(c+d+t+s+h)}{z} - (B+S)f = 0$$

$$Sf - \frac{Vg(c+d+t+s+h)}{z}-Bg = 0$$

$$\frac{Vg(c+d+t+s+h)}{z} + Ss - (B+C+E)h = 0$$

$$Fd + \frac{Ve(c+d+t+s+h)}{z} - (B+C+H+T)t = 0$$

$$Ht + \frac{Vf(c+d+t+s+h)}{z} - (U+B+C+S+S)s = 0$$

$$Tt + \frac{W(b+d)x}{z} - (B+H+Y)u = 0$$

$$Us - (S+B)v + Hu - \frac{HvY}{H+S} = 0$$

$$S(s+v) - Bw + Zy+ Eh = 0$$

$$Ec - (\frac{W(b+d)}{z}+B)x = 0$$

$$Y(u + \frac{H}{H+S})v - (B+X)y- Zy = 0$$

WHERE:

$$z = a + b + c + d + e + f + g + h + s + t + u + v + w + x + y$$

AND:

$$ a,b,c,d,e,f,g,h,s,t,u,v,w,x,y,A,B,C,D,E,F,G,H,S,T,U,V,W,X,Y,Z > 0 $$

I hope someone can help, considering all the effort I have put in!! Thanks!